This is really exciting :-)
What’s your end goal? More Beethoven etc? Or to play versions of favourite old songs/tunes etc?
If you want to play any classical pieces, then reading music is going to become critical at some point, and the ability to pick up a book of pieces and bash through them of your own accord is fabulous.
However, often starting to play and read music all at the same time can slow you down on the actual playing side…
I would strongly recommend getting some input from a teacher who has experience of teaching others in your situation. There is a balance to be struck between teaching you what middle C looks like in the music, and playing more interesting pieces that keep you interested as an adult. An understanding of chords etc will help you to play more interesting pieces sooner. The basic triad (which in the music is shown with a note on a line, the line above and the line above that, OR with a note on a space, the space above and the space above that) is a great shape to get used to – eg. notes CEG.
On the chord front, a simple chord progression to learn is a C triad (CEG), followed by an F triad (FAC), followed by a G triad (up one to GBD) then returning to the original C triad. (All of these chords use just the white keys.)
If you imagin the C triad as being chord 1 (normally shown with roman numeral I) – named because C is the first note of the scale in that particular key. The F triad is four notes higher, so is chord IV. Up one to the G triad takes you to chord V. Then returning to the original chord, chord I. So you have this chord pattern: I – IV – V – I. When you learn different keys (ie where the first note of the scale starts on a different note, which will affect the combination of white and black keys you play) this same chord progression will work.
Having some input from a teacher will also help you with how to hold your hands when you play, how to navigate your way around the notes, making best use of your fingers, and not giving yourself any injuries in the process.
If lessons are out of the question, for any reason, then youtube provides an incredible amount of inputs on learning any instruments, and if you are self motivated you can get quite far in this way. If you want to run any videos you find past me feel free to pm them to me. (I teach harp for a living, but also play piano, violin and viola to a high standard.)